Magnetic resonance imaging (MRI) optimized chemical-shift excitation

ABSTRACT

A magnetic resonance imaging (MRI) system ( 100 ) performs optimized chemical-shift excitation. A computer system ( 110 ) performs a constrained numerical optimization to determine radio frequency (RF) pulse amplitudes, phase angles, and interpulse intervals for a binomial-like RF pulse sequence that will excite magnetization ( 41 ) of a selective one of two chemical species, such as water and fat for example, of a subject ( 102 ) in relatively less time and that may therefore be used at lower magnetic fields. A static magnet ( 132 ) produces a magnetic field along a predetermined axis relative to the subject Pulse sequence apparatus ( 134, 152, 154, 156, 158 ) creates magnetic field gradients with the magnetic field, applies RF pulsed magnetic fields, and receives resulting RF magnetic resonance (MR) signals. Pulse sequence control apparatus ( 142 ) controls the pulse sequence apparatus to apply the binomial-like RF pulse sequence to the subject. The computer system reconstructs an image from received RF MR signals resulting from application of the binomial-like RF pulse sequence.

This patent application claims the benefit of the Sep. 26, 1997 filingdate of U.S. Provisional Application No. 60/060,184, which is hereinincorporated by reference.

FIELD OF THE INVENTION

The present invention relates generally to the field of magneticresonance imaging (MRI). More particularly, the present inventionrelates to the field of MRI chemical-shift excitation.

BACKGROUND OF THE INVENTION

In a typical magnetic resonance imaging MRI) system, a subject such as ahuman body is placed in a static magnetic field such that selectednuclear magnetic dipoles of the subject preferentially align with themagnetic field. The MRI system then applies radio frequency (RF) pulsedmagnetic fields to cause magnetic resonance of the preferentiallyaligned dipoles and detects RF magnetic resonance (MR) signals from theresonating dipoles for reconstruction into an image representation. TheMRI system typically scans the region to be imaged by applying RF pulsesequences to the subject while imposing time-varying magnetic fieldgradients with the static magnetic field.

In imaging most tissues with MRI, the hydrogen protons from water arepreferably detected as most soft tissues are composed of greater thanapproximately eighty percent water. Unfortunately, fat is also largelycomposed of hydrogen protons and may therefore appear as an unwanted orunnecessary component in many hydrogen MR images. A variety of methodshave been developed to help eliminate the effect of fat magnetizationfrom hydrogen MR images and thereby improve the contrast between normaland pathologic tissue in a variety of anatomic locations such as, forexample, the liver and pancreas, the orbits, the breast, bone marrow,and the coronary arteries. Water excitation methods apply an RF pulsesequence to tip water magnetization and not fat magnetization fordetection. Fat suppression methods apply an RF pulse sequence to tip fatmagnetization and not water magnetization, eliminate the fatmagnetization, and then excite the water magnetization for detection.Such methods are able to tip water and fat magnetization in a selectivemanner because of the chemical shift difference in resonant frequencybetween water protons and protons in the methylene (—CH₂) groups of fatmolecules.

The chemical shift difference between two chemical species in whichexcitation of one and elimination of the other is desired is given by δin parts per million (ppm). For water and fat protons, the chemicalshift difference is approximately 3.5 ppm in accordance with thefollowing equations: $\begin{matrix}{\omega_{water} = {{\gamma \quad B_{0}} = \quad {{\sim 2}{\pi \left( {64.05\quad {megaHertz}\quad ({MHz})} \right)}}}} & {\quad {{{at}\quad B_{0}} = {{\sim 1.5}\quad {Tesla}\quad {or}}}} \\{= \quad {{\sim 2}{\pi \left( {8.5\quad {MHz}} \right)}}} & {\quad {{{at}\quad B_{0}} = {{\sim 0.2}\quad {Tesla}}}} \\{{\Delta \quad \omega_{{water}\text{-}{fat}}} = \quad {{{\sim 2}{\pi \left( {64.05\quad {MHz}} \right)}\delta}\quad = {{\sim 2}{\pi \left( {224\quad {Hz}} \right)}}}} & {\quad {{{at}\quad B_{0}} = {{\sim 1.5}\quad {Tesla}\quad {or}}}} \\{= \quad {{{\sim 2}{\pi \left( {8.5\quad {MHz}} \right)}\delta}\quad = {{\sim 2}{\pi \left( {29.75\quad {Hz}} \right)}}}} & {\quad {{{at}\quad B_{0}} = {{\sim 0.2}\quad {Tesla}}}}\end{matrix}$

where ω is the Larmor frequency of the nuclei of interest, γ is thegyromagnetic ratio of the nuclei of interest, and B₀ is the appliedstatic magnetic field.

One common fat suppression method applies binomial sets of RF pulses atspecific amplitudes and specific interpulse intervals to tip fatmagnetization into the transverse or detection plane while restoringwater magnetization to the longitudinal axis. The amplitudes of the RFpulses are set such that their sum is approximately zero when observedby a water molecule (i.e., on resonance), and the duration of eachinterpulse interval is set, for example, to π/Δω=˜1/(448 Hz) at B₀=1.5Tesla=˜2.2 milliseconds (ms) such that the water and fat protons precessby approximately 180° or π radians with respect to one another. Once inthe detection plane, the fat magnetization may be spoiled or destroyed.A selective RF pulse may then be applied to tip the remaininglongitudinal magnetization into the detection plane. As the timeinterval between the tipping of fat magnetization into the detectionplane and spoiling is relatively short, the remaining longitudinalmagnetization tipped by the selective RF pulse is substantially allwater magnetization. Exemplary prior art binomial RF pulse sequencesinclude 1-(-1), 1-(-2)-1, and 1-(-3)-3-(-1) sequences.

The application of a prior art binomial 1-(-1) RF pulse sequence for fatsuppression is illustrated in graph form in FIGS. 1A, 1B, 1C, 1D, and1E. As illustrated in FIG. 1A, water magnetization 11 and fatmagnetization 12 are initially aligned with the static magnetic field B₀along the z-axis at equilibrium. A first RF pulse in the 1-(-1) sequencetips both water magnetization 11 and fat magnetization 12 byapproximately 45° as illustrated in FIG. 1B. During an interpulseinterval of approximately 2.2 ms for B₀=˜1.5 Tesla, fat magnetization 12precesses by rotating approximately 180° about the z-axis such thatwater magnetization 11 and fat magnetization 12 are approximately 180°out of phase as illustrated in FIG. 1C. A second RF pulse in the 1-(-1)sequence tips both water magnetization 11 and fat magnetization 12 byapproximately −45°, restoring water magnetization 11 to the z-axis whiletipping fat magnetization 12 into the detection plane as illustrated inFIG. 1D. Fat magnetization 12 is then spoiled by a magnetic fieldgradient pulse as illustrated in FIG. 1E, and water magnetization 11 maythen be tipped from the z-axis into the detection plane by a selectiveRF pulse.

Adding more RF pulses in a binomial sequence helps improve the spectralwidth of the saturation in an inhomogeneous magnetic field. At B₀=˜1.5Tesla, a binomial 1-3-3-1 RF pulse sequence, for example, may be usedfor fat suppression.

Applying binomial sets of RF pulses in relatively lower magnetic fields,however, incurs relatively longer repetition times TR and therefore scantimes as the duration of each interpulse interval is inverselyproportional to the strength of the magnetic field B₀. At B₀=˜0.2 Tesla,for example, a binomial RF pulse sequence requires an approximately 16.8ms interpulse interval as compared to the approximately 2.2 msinterpulse interval required at B₀=˜1.5 Tesla. For longer pulsesequences that are required for adequate suppression in an inhomogeneousmagnetic field, the time penalty incurred is too great for many imagingapplications. A binomial 1-3-3-1 RF pulse sequence, for example,requires approximately 50 ms in total interpulse interval time atB₀=˜0.2 Tesla.

Also, the effectiveness of binomial RF pulse sequences in suppressingfat may be compromised in relatively lower magnetic fields as therelatively longer interpulse intervals together with the reducedrelaxation time T1 for fat in the lower magnetic field allow significantfat magnetization regrowth. Relatively longer interpulse intervals alsoallow greater water magnetization decay as determined by the relaxationtime T2 for water.

Another common fat suppression method relies upon the regrowth of fatmagnetization. Fat and water magnetization regrow at different rates asdetermined by their respective relaxation times T1. Followingapplication of an inverting RF pulse, regrown magnetization willeffectively cancel the inverted magnetization after a certain timeperiod TI=ln(2)*T1=˜0.693*T1.

The application of a prior art inversion recovery RF pulse sequence forfat suppression is illustrated in graph form in FIGS. 2A, 2B, and 2C. Asillustrated in FIG. 2A, water magnetization 21 and fat magnetization 22are initially aligned with the static magnetic field B₀ along the z-axisat equilibrium. An inverting RF pulse tips both water magnetization 21and fat magnetization 22 by approximately 180° as illustrated in FIG.2B. After TI=˜160 ms at B₀=˜1.5 Tesla or TI=˜110 ms at B₀=˜0.2 Tesla,fat magnetization regrowth 23 effectively cancels inverted fatmagnetization 22 as illustrated in FIG. 2C. Water magnetization 21 maythen be tipped into the detection plane by a selective RF pulse.

At TI=˜110 ms or ˜160 ms, the time required for fat magnetizationregrowth incurs relatively longer repetition times TR and therefore scantimes. Inversion methods for fat suppression may also suppress themagnetization from tissues having a relaxation time T1 comparable tothat of fat and alter the contrast between tissues from that normallyachieved independently from the spin-echo or gradient-echo portion ofthe scan.

SUMMARY OF THE INVENTION

In accordance with the present invention, a method determines a radiofrequency (RF) pulse sequence of N RE pulses and N−1 interpulseinterval(s) for use in magnetic resonance imaging (MRI) of at least aportion of a subject comprising two chemical species, such as water andfat for example, having a chemical shift difference in resonantfrequency. The number N of RF pulses is an integer greater than one andmay be greater than or equal to three, for example.

For the method, a numerical optimization is performed to determine anamplitude and phase angle for each of the N RF pulses and a duration foreach of the N−1 interpulse interval(s) so as to excite magnetization ofa selective one of the two chemical species for MRI detection uponapplication of the RF pulse sequence to at least a portion of thesubject.

A total duration of the RF pulse sequence may be constrained inperforming the optimization. The optimization may be performed so as tohelp minimize magnetization of the selective one of the two chemicalspecies along a predetermined axis and help maximize magnetization ofthe other one of the two chemical species along the predetermined axisupon application of the RF pulse sequence to at least a portion of thesubject while constraining the total duration of the RF pulse sequence.

The optimization may also be performed so as to help minimize a totalduration of the RF pulse sequence while constraining magnetizationexcitation of the selective one of the two chemical species for MRIdetection upon application of the RF pulse sequence to at least aportion of the subject. The optimization may be performed so as to helpminimize total interpulse interval time while constraining magnetizationexcitation of the selective one of the two chemical species for MRIdetection upon application of the RF pulse sequence to at least aportion of the subject. Magnetization of each of the two chemicalspecies along a predetermined axis may be constrained in performing theoptimization.

The optimization may further constrain total interpulse interval time,the duration of each interpulse interval, the phase angle for each RFpulse, and/or a magnetization tip angle to be effectuated by each RFpulse upon application to at least a portion of the subject.

The determined RF pulse sequence may be applied to at least a portion ofthe subject, and an image may be reconstructed from resulting RFmagnetic resonance (MR) signals detected from at least a portion of thesubject.

Also in accordance with the present invention, a magnetic resonanceimaging (MRI) system comprises a static magnet, pulse sequenceapparatus, pulse sequence control apparatus, and a computer system.

The static magnet produces a magnetic field along a predetermined axisrelative to at least a portion of the subject in an examination region.The magnetic field may be approximately 0.2 Tesla, for example. Thepulse sequence apparatus creates magnetic field gradients in theexamination region, applies radio frequency (RF) pulsed magnetic fieldsin the examination region, and receives RF magnetic resonance (MR)signals from the examination region. The pulse sequence controlapparatus controls the pulse sequence apparatus to apply an RF pulsesequence in the examination region so as to excite magnetization of aselective one of the two chemical species. The RF pulse sequence isdetermined in accordance with the numerical optimization which may beperformed by the computer system. The computer system reconstructs animage from received RF MR signals resulting from application of the RFpulse sequence in the examination region.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example and notlimitation in the figures of the accompanying drawings, in which likereferences indicate similar elements and in which:

FIGS. 1A, 1B, 1C, 1D, and 1E illustrate in graph form water and fatmagnetization subjected to a prior art binomial 1-(-1) RF pulse sequencefor fat suppression;

FIGS. 2A, 2B, and 2C illustrate in graph form water and fatmagnetization subjected to a prior art inversion recovery RF pulsesequence for fat suppression;

FIG. 3 illustrates in block diagram form an exemplary magnetic resonanceimaging (MRI) system for performing optimized chemical-shift excitationin accordance with the present invention; and

FIGS. 4A, 4B, 4C, 4D, 4E, and 4F illustrate in graph form water and fatmagnetization subjected to an exemplary binomial-like RF pulse sequencefor water excitation in accordance with the present invention.

DETAILED DESCRIPTION

A magnetic resonance imaging (MRI) system performs optimizedchemical-shift excitation. A computer system performs a numericaloptimization for the MRI system to determine a set of parametersincluding radio frequency (RF) pulse amplitudes or strengths, RF pulsephase angles, and interpulse intervals for a binomial-like RF pulsesequence of N RF pulses that will excite a desired nuclear or chemicalspecies, such as water for example. By allowing the RF pulse tip angles,RF pulse phase angles, and interpulse intervals to vary, the computersystem may determine a binomial-like RF pulse sequence that requiresrelatively less time and that may therefore be used by the MRI systemfor applications at relatively lower magnetic fields, such as at B₀=˜0.2Tesla for example. The optimization performed by the computer system mayconstrain and/or help minimize the total interpulse interval time toensure the resulting binomial-like RF pulse sequence requires relativelyless time and to help minimize T1 and/or T2 relaxation.

Exemplary Magnetic Resonance Imaging (MRI) System

FIG. 3 illustrates an exemplary magnetic resonance imaging (MRI) system100 for performing optimized chemical-shift excitation in accordancewith the present invention.

The operation of MRI system 100 is controlled by a computer system 110.A console 120 comprising a control panel 122 and a display 124communicates with computer system 110 to enable an operator to controlthe production and display of MRI images on display 124.

To produce images with MRI system 100, at least a portion of a subject102 of interest is placed within an examination region 104. A staticmagnet 132 produces a substantially uniform, temporally constantmagnetic field along a desired z-axis such that selected nuclearmagnetic dipoles of subject 102 within examination region 104preferentially align with the magnetic field. Although illustrated as ahuman subject, subject 102 may be an animal subject or any othersuitable sample.

Computer system 110 communicates with a pulse program generator 142 tocontrol a set of G_(x), G_(y), G_(z) gradient amplifiers and coils 134,a radio frequency (RF) transmitter 152, and an RF receiver 154 so as tocarry out a desired MRI scan sequence.

RF transmitter 152 transmits RF pulses into examination region 104 usingRF coils 156 to cause magnetic resonance of the preferentially aligneddipoles of subject 102 within examination region 104. RF receiver 154receives RF magnetic resonance (MR) signals detected by RF coils 156from the resonating dipoles of examination region 104. Pulse programgenerator 142 also controls a transmit/receive (T/R) switch 158selectively connecting RF transmitter 152 and RF receiver 154 to RFcoils 156. Separate transmit and receive RF coils may also be used,obviating any need for T/R switch 158. Computer system 110 comprises ananalog-to-digital converter 144 to receive the RF MR signals from RFreceiver 154 in digital form and processes the digitized RF MR signalsto reconstruct an image representation for display on display 124.

Gradient amplifiers and coils 134 impose time-varying magnetic fieldgradients with the static magnetic field along mutually orthogonal x, y,z-axes to spatially encode the received RF MR signals. In this manner,images may be scanned along a particular one of contiguous parallelslice-volumes p, q, . . . , z defined in examination region 104.

Computer system 110 loads software or program code defining differentMRI pulse sequences into writable control storage areas of pulse programgenerator 142. Pulse program generator 142 executes program codecorresponding to a given pulse sequence to provide suitable signals thatcontrol the operation of RF transmitter 152, RF receiver 154, T/R switch158, and gradient amplifiers and coils 134 and thereby effectuate thegiven pulse sequence. Computer system 110 can specify and effectuate anysuitable MRI pulse sequence for MRI system 100 as desired.

Optimized Hybrid Binomial RF Pulse Scheme

In accordance with the present invention, computer system 110 performs anumerical optimization to determine a set of parameters including RFpulse amplitudes or strengths, RF pulse phase angles, and interpulseintervals for a binomial-like RF pulse sequence of N RF pulses that willexcite a desired chemical species, such as water for example, of atleast a portion of subject 102. The number N of RF pulses is an integergreater than one and may be two, three, or four, for example. Althoughdescribed as determining binomial-like RF pulse sequences for selectivefat/water excitation, the present invention may be used for selectiveexcitation of any other suitable chemical species having a chemicalshift difference in resonance frequency.

The numerical optimization problem for one embodiment is formulated asthe product of a series of rotation/transformation matrices.

The xyz magnetization for water and fat of subject 102 is described as:$\begin{matrix}{M = {\begin{matrix}M_{x}^{water} \\M_{y}^{water} \\M_{z}^{water} \\M_{x}^{fat} \\M_{y}^{fat} \\M_{z}^{fat}\end{matrix}}} & {{Equation}\quad 1}\end{matrix}$

where M_(x), M_(y), and M_(z) represent magnetization along the x, y,and z axes, respectively.

A RF pulse rotation matrix is described as: $\begin{matrix}{{R\left( \alpha_{n} \right)} = {\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & {\cos \left( \alpha_{n} \right)} & {\sin \left( \alpha_{n} \right)} & 0 & 0 & 0 \\0 & {- {\sin \left( \alpha_{n} \right)}} & {\cos \left( \alpha_{n} \right)} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & {\cos \left( \alpha_{n} \right)} & {\sin \left( \alpha_{n} \right)} \\0 & 0 & 0 & 0 & {- {\sin \left( \alpha_{n} \right)}} & {\cos \left( \alpha_{n} \right)}\end{matrix}}} & {{Equation}\quad 2}\end{matrix}$

where α_(n) is the angle at which the nth RF pulse of the binomial-likeRF pulse sequence is to tip the water and fat magnetization.

The precession of the water and fat magnetization during an interpulseinterval, presuming that fat precesses at a negative angular frequencyrelative to water, is described as: $\begin{matrix}{{P\left( \tau_{n} \right)} = {\begin{matrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & {\cos \left( {k\quad \tau_{n}} \right)} & {\sin \left( {k\quad \tau_{n}} \right)} & 0 \\0 & 0 & 0 & {- {\sin \left( {k\quad \tau_{n}} \right)}} & {\cos \left( {k\quad \tau_{n}} \right)} & 0 \\0 & 0 & 0 & 0 & 0 & 1\end{matrix}}} & {{Equation}\quad 3}\end{matrix}$

where τ_(n) is the duration of the nth interpulse interval of thebinomial-like RF pulse sequence and k is a constant that relatesinterpulse interval time to a dephasing angle between fat and water.

The transformation of transverse magnetization from the conventionalrotating reference frame coordinate system (x′,y′) to one aligned withan upcoming RF pulse is described as: $\begin{matrix}{{~~}{{\Phi_{n}\left( \phi_{n} \right)} = {\begin{matrix}{\cos \left( \phi_{n} \right)} & {\sin \left( \phi_{n} \right)} & 0 & 0 & 0 & 0 \\{- {\sin \left( \phi_{n} \right)}} & {\cos \left( \phi_{n} \right)} & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & {\cos \left( \phi_{n} \right)} & {\sin \left( \phi_{n} \right)} & 0 \\0 & 0 & 0 & {- {\sin \left( \phi_{n} \right)}} & {\cos \left( \phi_{n} \right)} & 0 \\0 & 0 & 0 & 0 & 0 & 1\end{matrix}}}} & {{Equation}\quad 4}\end{matrix}$

where (ψ_(n) is the phase angle of the nth RF pulse of the binomial-likeRF pulse sequence.

That is, Φ is a rotation matrix used to express the current M_(xy) interms of components parallel and perpendicular to the phase modulated RFpulse. For one embodiment, the first RF pulse phase angle ψ₁ is set to0° while the remaining phase angles ψ_(n) for all subsequent RF pulsesof the binomial-like RF pulse sequence are set relative to this firstphase angle ψ₁.

The water and fat magnetization following the first RF pulse and firstinterpulse interval yet prior to the second RF pulse of thebinomial-like RF pulse sequence is described as follows.

⁺ M(α₁)=P(τ₁)R(α₁)M  Equation 5

The water and fat magnetization following the second RF pulse and secondinterpulse interval yet prior to the third RF pulse of the binomial-likeRF pulse sequence is described as follows.

⁺ M(α₂)=P(τ₂)·Φ⁻¹(ψ₂)R(α₂)Φ(ψ₂)⁺ M(α₁)  Equation 6

For each subsequent RF pulse and interpulse interval, the water and fatmagnetization following the nth RF pulse and the nth interpulse intervalyet prior to the (n+1)th RF pulse of the binomial-like RF pulse sequenceis similarly described as follows.

⁺ M(α_(n))=P(τ_(n))·Φ⁻¹(ψ_(n))R(α_(n))Φ(ψ_(n))⁺ M(α_(n−1))  Equation 7

For a binomial-like RF pulse sequence of N=3 RF pulses, the final waterand fat magnetization is described as follows.

⁺ M(α₃)=R(α₃)Φ(ψ₃)P(τ₂)Φ⁻¹(ψ₂)R(α₂)Φ(ψ₂)P(τ₁)R(α₁)M  Equation 8

In accordance with equations 1-8, computer system 110 determines anoptimal or near-optimal set of RF pulse tip angles α_(n), interpulseintervals τ_(n), and RF pulse phase angles ψ_(n) for a binomial-like RFpulse sequence of N RF pulses that will tip water magnetization into thedetection plane and restore fat magnetization to the longitudinal axis.By allowing the RF pulse tip angles α_(n), interpulse intervals τ_(n),and RF pulse phase angles ψ_(n) to vary, computer system 110 maydetermine a binomial-like RF pulse sequence that requires relativelyless time and that may therefore be used by MRI system 100 forapplications at relatively lower magnetic fields, such as at B₀=˜0.2Tesla for example.

Computer system 110 for one embodiment attempts to minimize the watermagnetization M_(z) ^(water) along the z-axis and maximize the fatmagnetization M_(z) ^(fat) along the z-axis in determining the set ofparameters for a binomial-like RF pulse sequence of N RF pulses. As oneexample, computer system 110 attempts to minimize the function f asfollows:

min f=(⁺ M _(z) ^(water)(α_(N)))²+(1−⁺ M _(z) ^(fat)(α_(N)))²=minf=M(3,1)²+(1−M(6,1))² after the Nth pulse  Equation 9

in determining the set of parameters. The function f is the squareddeviation from the condition when the water magnetization along thez-axis is zero, indicating all water magnetization is in the transverseplane, and when the fat magnetization along the z-axis is one,indicating all fat magnetization is restored along the z-axis.

The optimization performed by computer system 110 for one embodimentconstrains the total sequence time in determining the set of parametersto ensure the resulting binomial-like RF pulse sequence requiresrelatively less time. The total sequence time may be constrained, forexample, by constraining the duration of each interpulse interval withina predetermined time range and the total interpulse interval time withina predetermined time range as follows.

C 1: τ_(min)≦τ_(n)≦τ_(max) for 1≦n≦N−1

C 2: TT _(min)≦Στ_(n) ≦TT _(max) for 1≦n≦N−1

Under constraint C1, the minimum allowable interpulse interval τ_(n) fora binomial-like RF pulse sequence is τ_(min), and the maximum allowableinterpulse interval τ_(n) for a binomial-like RF pulse sequence isτ_(max). The minimum and maximum interpulse interval times τ_(min) andτ_(max) may be set to any suitable value. As one example where eachinterpulse interval τ_(n) is measured from the centers of the nth and(n+1)th RF pulses, the minimum interpulse interval τ_(min) may be set tothe RF pulse duration T which may have suitable value, such as 1.28 msfor N=3 for example, and the maximum interpulse interval τ_(max) may beset to ∞.

Under constraint C2, the minimum allowable total interpulse intervaltime Στ_(n) for a binomial-like RF pulse sequence is TT_(min), and themaximum allowable total interpulse interval time Στ_(n) for abinomial-like RF pulse sequence is TT_(max). The minimum and maximumtotal interpulse interval times TT_(min) and TT_(max) may be set to anysuitable value. As one example where each interpulse interval τ_(n) ismeasured from the centers of the nth and (n+1)th RF pulses, the minimumtotal interpulse interval time TT_(max) may be set to (N−1)*T, and themaximum total interpulse interval time TT_(max) may be set to anysuitable greater value. The maximum total interpulse interval timeTT_(max) may be set by an operator of MRI system 100 so as to reflectthe maximum tolerable repetition time TR for a particular MRIapplication. As one example for N=3, TT_(max) may be set to 20 ms. Themaximum total interpulse interval time TT_(max) may be set such thatΣτ_(n) is less than the duration of the interpulse interval for a singledephasing in typical binomial methods, or k*Στ_(n)<180°. By constrainingthe total interpulse interval time Στ_(n) the optimization performed bycomputer system 110 helps to minimize T1 and/or T2 relaxation andtherefore helps alleviate concerns of fat magnetization regrowth and/orsignal loss during each interpulse interval.

The optimization performed by computer system 110 may also constrain thevalues for the RF pulse tip angles α_(n) and RF pulse phase angles ψ_(n)as follows.

C 3: α_(min)≦α_(n)≦α_(max) for 1≦n≦N

C 4: ψ_(min)≦ψ_(n)≦ψ_(max) for 1≦n≦N

Under constraint C3, the minimum allowable RF pulse tip angle α_(n) isα_(min), and the maximum allowable RF pulse tip angle α_(n) is α_(max).The minimum and maximum RF pulse tip angles α_(min) and α_(max) may beset to any suitable value. Under constraint C4, the minimum allowable RFpulse phase angle ψ_(n) is ψ_(min), and the maximum allowable RF pulsephase angle ψ_(n) is ψ_(max). The minimum and maximum RF pulse phaseangles ψ_(min) and ψ_(max) may be set to any suitable value. As oneexample, the minimum RF pulse tip angle α_(min) may be set to 0°, themaximum RF pulse tip angle α_(max) may be set to 180°, the minimum RFpulse phase angle ψ_(min) may be set to −180°, and the maximum RF pulsephase angle ψ_(max) may be set to 180° so that the RF pulses for abinomial-like RF pulse sequence may perform any possible rotation of thewater and fat magnetization.

Computer system 110 for another embodiment attempts to minimize thetotal interpulse interval times as follows: $\begin{matrix}{\min {\sum\limits_{n = 1}^{N - 1}\quad \tau_{n}}} & {{Equation}\quad 10}\end{matrix}$

in determining the set of parameters for a binomial-like RF pulsesequence of N RF pulses. This optimization performed by computer system110 may constrain the final water magnetization M_(z) ^(water) along thez-axis to a value less than or equal to a predetermined amount K1 and/orthe final fat magnetization M_(z) ^(fat) along the z-axis to a valuegreater than or equal to a predetermined amount K2 as follows.

C 5:⁺ M _(z) ^(water)(α_(N))≦K 1

C 6:⁺ M _(z) ^(fat)(α_(N))≦K 2

K1 and K2 may each have any suitable value. For one embodiment where themaximum water magnetization M_(z) ^(water) along the z-axis and themaximum fat magnetization M_(z) ^(fat) along the z-axis are eachnormalized to 1.0 for simplicity, K1 may be approximately 0.05, forexample, and K2 may be approximately 0.95, for example. Computer system110 may attempt to minimize the total interpulse interval time in thismanner to better ensure minimal T1 and/or T2 relaxation.

In addition to constraints C5 and C6, computer system 110 may use one ormore of the constraints C1-C4 in attempting to minimize the totalinterpulse interval time for a binomial-like RF pulse sequence.

Computer system 110 may perform the optimizations for equations 9 and 10and constraints C1-C6 using any suitable nonlinearly constrainedoptimization algorithm. Computer system 110 for one embodiment may usethe nonlinearly constrained optimization algorithm in the OptimizationToolbox of the Matlab 5.2 programming environment provided by TheMathworks of Nattick, Mass.

Once the set of parameters for a binomial-like RF pulse sequence havebeen determined, computer system 110 may then control MRI system 100 toapply the binomial-like RF pulse sequence to subject 102. Computersystem 110 may load suitable program code defining the binomial-like RFpulse sequence into pulse program generator 142. Pulse program generator142 may then execute the program code to thereby effectuate thebinomial-like RF pulse sequence.

Although described as being determined by computer system 110, anysuitable computer system, such as a personal computer for example, maybe used to determine the set of parameters for a binomial-like RF pulsesequence. The determined set of parameters may then be programmed orentered into computer system 110 in a suitable manner using console 120,for example.

The application of an exemplary binomial-like RF pulse sequence of N=3pulses as determined by computer system 110 is illustrated in graph formin FIGS. 4A, 4B, 4C, 4D, 4E, and 4F. As illustrated in FIG. 4A, watermagnetization 41 and fat magnetization 42 are initially aligned with thestatic magnetic field B₀ along the z-axis at equilibrium. The first RFpulse, characterized by a tip angle of α₁° and a phase angle of ψ₁=0°,tips both water magnetization 41 and fat magnetization 42 by α₁° asillustrated in FIG. 4B. During the first interpulse interval τ₁, fatmagnetization 42 precesses by rotating (k*τ₁)° about the z-axis suchthat water magnetization 41 and fat magnetization 42 are (k*τ₁)° out ofphase as illustrated in FIG. 4C. The second RF pulse, characterized by atip angle of α₂° and a phase angle of ψ₂°, tips both water magnetization41 and fat magnetization 42 by α₂° as illustrated in FIG. 4D. During thesecond interpulse interval τ₂, water magnetization 41 and fatmagnetization 42 precess (k*τ₂)° out of phase from their relativeposition following the second RF pulse, as illustrated in FIG. 4E. Thethird RF pulse, characterized by a tip angle of α₃° and a phase angle ofψ₃°, tips both water magnetization 41 and fat magnetization 42 by α₃°such that water magnetization 41 is tipped into the detection plane andfat magnetization 42 is restored to the z-axis as illustrated in FIG.4F.

MRI system 100 may apply binomial-like RF pulse sequences at anysuitable magnetic field B₀. As a binomial-like RF pulse sequence may bedetermined so as to require relatively less time with minimal T1 and/orT2 relaxation as compared to typical binomial or inversion recoverysequences, MRI system 100 may apply binomial-like RF pulse sequences atrelatively lower magnetic fields, such as at B₀=˜0.2 Tesla for example,to enhance the conspicuity of lesions that occur in or near fat inimaging the orbits, skull base, or appendicular areas, for example. Toaccommodate water excitation in a pulse sequence and therefore theincreased repetition time TR, MRI system 100 may allow the scan TR andhence scan time to increase or may reduce the number of slices inexamination region 104 in interleaved multi-slice experiments whilemaintaining TR substantially constant.

Although described in connection with MRI system 100 as illustrated inFIG. 3, any suitable MRI system may be used. One suitable MRI system isa Siemens Magnetom Opens® 0.2T resistive imager, manufactured by SiemensMedical Systems of Erlangen, Germany, with Numaris V3.5.1 software, a 26ms/500 ms spin-echo sequence, and a FLASH 9 ms/45 ms (TRITE).

In addition to water excitation, computer system 110 may also determinebinomial-like RF pulse sequences to suppress fat magnetization. Computersystem 110 may similarly determine the set of parameters for abinomial-like RF pulse sequence that will tip fat magnetization into thedetection plane and restore water magnetization to the longitudinal axisso that the fat magnetization may be spoiled as described in connectionwith FIG. 1E. The water magnetization may then be tipped into thedetection plane by a selective RF pulse.

In the foregoing description, the invention has been described withreference to specific exemplary embodiments thereof. It will, however,be evident that various modifications and changes may be made theretowithout departing from the broader spirit or scope of the presentinvention as defined in the appended claims. The specification anddrawings are, accordingly, to be regarded in an illustrative rather thana restrictive sense.

What is claimed is:
 1. A computer-implemented method for determining aradio frequency (RF) pulse sequence of N RF pulses and N−1 interpulseinterval(s), where N is an integer greater than one, for use in magneticresonance imaging (MRI) of at least a portion of a subject comprisingtwo chemical species having a chemical shift difference in resonantfrequency, the method comprising the step of: performing a numericaloptimization to determine an amplitude and phase angle for each of the NRF pulses and a duration for each of the N−1 interpulse interval(s) soas to excite magnetization of a selective one of the two chemicalspecies for MRI detection upon application of the RF pulse sequence toat least a portion of the subject.
 2. The method of claim 1, where N isan integer greater than or equal to three.
 3. The method of claim 1,wherein the performing step comprises the step of constraining totalinterpulse interval time and/or the duration of each interpulseinterval.
 4. The method of claim 1, wherein the performing stepcomprises the step of constraining the phase angle for each RF pulseand/or a magnetization tip angle to be effectuated by each RF pulse uponapplication to at least a portion of the subject.
 5. The method of claim1, in combination with the additional steps of: applying the determinedRF pulse sequence to at least a portion of the subject; andreconstructing an image from resulting RF magnetic resonance signalsdetected from at least a portion of the subject.
 6. The method of claim1, wherein the two chemical species are water and fat.
 7. Acomputer-implemented method for determining a radio frequency (RF) pulsesequence of N RF pulses and N−1 interpulse interval(s), where N is aninteger greater than one, for use in magnetic resonance imaging (MRI) ofat least a portion of a subject comprising two chemical species having achemical shift difference in resonant frequency, the method comprisingthe step of: performing a constrained numerical optimization todetermine an amplitude and phase angle for each of the N RF pulses and aduration for each of the N−1 interpulse interval(s) so as to excitemagnetization of a selective one of the two chemical species for MRIdetection upon application of the RF pulse sequence to at least aportion of the subject while constraining a total duration of the RFpulse sequence.
 8. The method of claim 7, wherein the performing stepcomprises the step of performing the constrained numerical optimizationso as to help minimize magnetization of the selective one of the twochemical species along a predetermined axis and help maximizemagnetization of the other one of the two chemical species along thepredetermined axis upon application of the RF pulse sequence to at leasta portion of the subject while constraining the total duration of the RFpulse sequence.
 9. The method of claim 7, wherein the performing stepcomprises the step of constraining total interpulse interval time and/orthe duration of each interpulse interval.
 10. The method of claim 7,wherein the performing step comprises the step of constraining the phaseangle for each RF pulse and/or a magnetization tip angle to beeffectuated by each RF pulse upon application to at least a portion ofthe subject.
 11. The method of claim 7, in combination with theadditional steps of: applying the determined RF pulse sequence to atleast a portion of the subject; and reconstructing an image fromresulting RF magnetic resonance signals detected from at least a portionof the subject.
 12. The method of claim 7, wherein the two chemicalspecies are water and fat.
 13. A computer-implemented method fordetermining a radio frequency (RF) pulse sequence of N RF pulses and N−1interpulse interval(s), where N is an integer greater than one, for usein magnetic resonance imaging (MRI) of at least a portion of a subjectcomprising two chemical species having a chemical shift difference inresonant frequency, the method comprising the step of: performing aconstrained numerical optimization to determine an amplitude and phaseangle for each of the N RF pulses and a duration for each of the N−1interpulse interval(s) so as to help minimize a total duration of the RFpulse sequence while constraining magnetization excitation of aselective one of the two chemical species for MRI detection uponapplication of the RF pulse sequence to at least a portion of thesubject.
 14. The method of claim 13, wherein the performing stepcomprises the step of performing the constrained numerical optimizationso as to help minimize total interpulse interval time while constrainingmagnetization excitation of the selective one of the two chemicalspecies for MRI detection upon application of the RF pulse sequence toat least a portion of the subject.
 15. The method of claim 13, whereinthe performing step comprises the step of constraining magnetization ofeach of the two chemical species along a predetermined axis.
 16. Themethod of claim 13, wherein the performing step comprises the step ofconstraining total interpulse interval time and/or the duration of eachinterpulse interval.
 17. The method of claim 13, wherein the performingstep comprises the step of constraining the phase angle for each RFpulse and/or a magnetization tip angle to be effectuated by each RFpulse upon application to at least a portion of the subject.
 18. Themethod of claim 13, in combination with the additional steps of:applying the determined RF pulse sequence to at least a portion of thesubject; and reconstructing an image from resulting RF magneticresonance signals detected from at least a portion of the subject. 19.The method of claim 13, wherein the two chemical species are water andfat.
 20. A magnetic resonance imaging (MRI) system comprising: a staticmagnet for producing a magnetic field along a predetermined axisrelative to at least a portion of a subject in an examination region,the subject comprising two chemical species having a chemical shiftdifference in resonant frequency; pulse sequence apparatus for creatingmagnetic field gradients in the examination region, for applying radiofrequency (RF) pulsed magnetic fields in the examination region, and forreceiving RF magnetic resonance (MR) signals from the examinationregion; pulse sequence control apparatus for controlling the pulsesequence apparatus to apply an RF pulse sequence in the examinationregion so as to excite magnetization of a selective one of the twochemical species, the RF pulse sequence having (i) N RF pulses eachhaving an amplitude and phase angle determined in accordance with anumerical optimization and (ii) N−1 interpulse interval(s) each having aduration determined in accordance with the numerical optimization, whereN is an integer greater than one; and a computer system forreconstructing an image from received RF MR signals resulting fromapplication of the RF pulse sequence in the examination region.
 21. TheMRI system of claim 20, where N is an integer greater than or equal tothree.
 22. The MRI system of claim 20, wherein each RF pulse amplitude,each RF pulse phase angle, and each interpulse interval duration isdetermined in accordance with the numerical optimization such that atotal duration of the RF pulse sequence is constrained.
 23. The MRIsystem of claim 22, wherein each RF pulse amplitude, each RF pulse phaseangle, and each interpulse interval duration is determined in accordancewith the numerical optimization so as to help minimize magnetization ofthe selective one of the two chemical species along the predeterminedaxis and help maximize magnetization of the other one of the twochemical species along the predetermined axis.
 24. The MRI system ofclaim 20, wherein each RF pulse amplitude, each RF pulse phase angle,and each interpulse interval duration is determined in accordance withthe numerical optimization so as to help minimize a total duration ofthe RF pulse sequence.
 25. The MRI system of claim 24, wherein each RFpulse amplitude, each RF pulse phase angle, and each interpulse intervalduration is determined in accordance with the numerical optimization soas to help minimize total interpulse interval time.
 26. The MRI systemof claim 24, wherein each RF pulse amplitude, each RF pulse phase angle,and each interpulse interval duration is determined in accordance withthe numerical optimization such that magnetization of the selective oneof the two chemical species along the predetermined axis is less than apredetermined value and such that magnetization of the other one of thetwo chemical species along the predetermined axis is greater than apredetermined value.
 27. The MRI system of claim 20, wherein each RFpulse amplitude, each RF pulse phase angle, and each interpulse intervalduration is determined in accordance with the numerical optimizationsuch that total interpulse interval time and/or each interpulse intervalduration is constrained.
 28. The MRI system of claim 20, wherein each RFpulse amplitude, each RF pulse phase angle, and each interpulse intervalduration is determined in accordance with the numerical optimizationsuch that each phase angle and/or a magnetization tip angle to beeffectuated by each RF pulse is constrained.
 29. The MRI system of claim20, wherein the computer system performs the numerical optimization todetermine each RF pulse amplitude, each RF pulse phase angle, and eachinterpulse interval duration.
 30. The MRI system of claim 20, whereinthe two chemical species are water and fat.
 31. The MU system of claim20, wherein the static magnet produces a magnetic field of approximately0.2 Tesla.